Search found 555 matches

by jaap
Thu Sep 09, 2021 4:45 pm
Forum: Clarifications on Project Euler Problems
Topic: Problem 762
Replies: 3
Views: 195

Re: Problem 762

Two things: Originally there is only one amoeba in the square (0,0). So the first amoeba is in the bottom-left corner. After N divisions there will be N+1 amoebas arranged in the grid. A division is a division of a single amoeba, not the division of an entire generation. When an amoebe splits, it di...
by jaap
Thu Aug 26, 2021 3:24 pm
Forum: Clarifications on Project Euler Problems
Topic: Problem 756
Replies: 9
Views: 701

Re: Problem 756

rsjw wrote: Thu Aug 26, 2021 2:54 pm I have trouble with the first example
E(Δ|k,100,50) = 2525/1326 ≈ 1.904223
Since Δ = S - S* f(k)=k is a monotonically-increasing function , then Δ < 0 , why won't the expected value be negative?
Will it be Δ = | S - S* |?
Take a closer look at what values X_m could take.
by jaap
Wed Aug 04, 2021 2:57 pm
Forum: Clarifications on Project Euler Problems
Topic: Problem 761
Replies: 9
Views: 756

Re: Problem 761

So if the swimmer starts swimming laps, the runner is going to gradually drop behind, and at some point the swimmer will reach a corner when the runner is diagonally opposite. When the moment arrives that the runner is half a laptime behind, why would that be exactly when the swimmer is at a corner...
by jaap
Fri Jul 23, 2021 3:39 pm
Forum: News, Suggestions, and FAQ
Topic: Errors/Warnings/Bugs
Replies: 647
Views: 226900

Re: Errors/Warnings/Bugs

The security certificate of projecteuler.chat seems to have expired today.
by jaap
Tue May 04, 2021 4:56 pm
Forum: Clarifications on Project Euler Problems
Topic: Problem 756
Replies: 9
Views: 701

Re: Problem 756

Uniformly distributed refers to the probability distribution, and means that when the m-tuple is chosen at random, every possible outcome is equally probable. See Uniform Distribution . Of course, you randomly choose only from the set of valid m-tuples (i.e. it must have m integers that are strictly...
by jaap
Fri Apr 30, 2021 1:16 pm
Forum: Clarifications on Project Euler Problems
Topic: Problem 147
Replies: 12
Views: 6107

Re: Problem 147

They are not sub-grids of each other. The question just asks you to examine one grid of each possible size up to some maximum size limit, and add their results together.
by jaap
Thu Mar 11, 2021 2:04 pm
Forum: Number Theory
Topic: Calculating modular inverses of p mod $2^p$
Replies: 2
Views: 1066

Re: Calculating modular inverses of p mod $2^p$

After some experimentation it turns out that if $p=2k+1$ then the inverse of $p$ mod $2^p$ is $\frac{k\cdot2^p + 1}{p}$. Clearly if that fraction is actually an integer, then it works as the inverse of $p$ mod $2^p$. To prove that it is an integer for prime $p$, you can use Fermat's little theorem (...
by jaap
Wed Mar 10, 2021 9:43 pm
Forum: News, Suggestions, and FAQ
Topic: How do I toggle Dark Mode?
Replies: 2
Views: 450

Re: How do I toggle Dark Mode?

In the Account tab scroll down to the section with Location/Language/Time Zone etc., change the Theme from Default to Dark or vice versa, and click the Update Details button.
by jaap
Sun Nov 29, 2020 10:05 pm
Forum: Clarifications on Project Euler Problems
Topic: Problem 273
Replies: 37
Views: 16409

Re: Problem 273

There's an 's' missing in 'integer' in the first line of the problem statement. And the same missing 's' in the same word on line 4. You could add an s, but it is also correct as is, since integer is being used here as an adjective rather than a noun (like "whole" instead of "whole n...
by jaap
Thu Nov 05, 2020 8:57 am
Forum: News, Suggestions, and FAQ
Topic: Idea for new Archives display filter
Replies: 11
Views: 2021

Re: Idea for new Archives display filter

You can currently filter the archives by All/Solved/Unsolved/Pinned. Any chance of adding a filter for problems which have a new forum post within the past day? You can already see those in the past day by the coloring, but it would be nice to collect them all tightly, rather than looking through 1...
by jaap
Thu Sep 24, 2020 2:33 pm
Forum: News, Suggestions, and FAQ
Topic: Errors/Warnings/Bugs
Replies: 647
Views: 226900

Re: Errors/Warnings/Bugs

Two minor irritations: 1. When you select and copy/paste the text of a PE problem, the MathJax is not selected and copied. I like to put the problem into a code comment at the top of my program for the problem, and that is more work now. It used to mostly copy the maths text, except for some weirdne...
by jaap
Fri Jul 24, 2020 8:37 am
Forum: News, Suggestions, and FAQ
Topic: Errors/Warnings/Bugs
Replies: 647
Views: 226900

Re: Errors/Warnings/Bugs

Hi, I am having trouble opening the thread for Problem 497. Chrome would load a few posts but when I scrolled down further, it became just a blank screen. Maths formulas were not rendered and code sections would not open. Thank you for reporting this. I cannot load the thread either: the Chrome tab...
by jaap
Tue Jun 30, 2020 2:51 pm
Forum: Clarifications on Project Euler Problems
Topic: Problem 059
Replies: 114
Views: 50533

Re: Problem 059

Hi! I also have trouble in getting "an OK - problem solved" although I'm like TristenR am pretty sure I've solved it. However, counting up the entries in the original file - I only get 1454... which is contrary to TristenRs 1455. What is the correct number here (in the original text file)...
by jaap
Tue Feb 25, 2020 6:32 am
Forum: Clarifications on Project Euler Problems
Topic: Problem 207
Replies: 8
Views: 6100

Re: Problem 207

...where $4^t$, $2^t$, and $k$ are all positive integers and $t$ is a real number. For any m ≥ 1 let P(m) be the proportion of such partitions that are perfect with k ≤ m . So there are two partitions, $4^1 = 2^1 + 2$ and $4^{1.5849625...} = 2^{1.5849625...} + 6$ with $k\le 6$, only one of which ha...
by jaap
Mon Feb 10, 2020 5:52 am
Forum: Clarifications on Project Euler Problems
Topic: Problem 701
Replies: 3
Views: 2714

Re: Problem 701

701 "Consider the maximum area of connected cells." Nowhere is "maximum area" defined. It's just the literal meaning. The largest possible area of a connected set of (black) cells. Wouldn't the largest possible area be W x H, i.e. the given square with every square a black squar...
by jaap
Sun Feb 09, 2020 7:52 pm
Forum: Clarifications on Project Euler Problems
Topic: Problem 701
Replies: 3
Views: 2714

Re: Problem 701

Junglemath wrote: Sun Feb 09, 2020 6:36 pm Problem 701 (View Problem)

"Consider the maximum area of connected cells."

Nowhere is "maximum area" defined.
It's just the literal meaning. The largest possible area of a connected set of (black) cells.
by jaap
Mon Feb 03, 2020 6:49 am
Forum: Clarifications on Project Euler Problems
Topic: problem 065
Replies: 33
Views: 13808

Re: problem 065

whatteaux wrote: Sun Feb 02, 2020 11:18 pm
jaap wrote: Fri Jan 31, 2020 12:44 pm But it is surprising that e's continued fraction has a pattern to it at all.
Did you mmean Pi, rather than e? E's has a pattern (as shown in this thread), whereas Pi's is patternless.
I'm saying that you would not expect a pattern for e, so it is surprising that there is one.
by jaap
Fri Jan 31, 2020 12:44 pm
Forum: Clarifications on Project Euler Problems
Topic: problem 065
Replies: 33
Views: 13808

Re: problem 065

In the problem statement it lists 2k as one of the components of the continued fraction, but nowhere is it stated what k is. Help? It is just there to indicate that the pattern shown in the first numbers continues. It shows what an arbitrary section of the list would look like. Here are some other ...
by jaap
Fri Jan 31, 2020 9:31 am
Forum: Clarifications on Project Euler Problems
Topic: problem 065
Replies: 33
Views: 13808

Re: problem 065

In the problem statement it lists 2k as one of the components of the continued fraction, but nowhere is it stated what k is. Help? It is just there to indicate that the pattern shown in the first numbers continues. It shows what an arbitrary section of the list would look like. Here are some other ...
by jaap
Fri Dec 20, 2019 5:23 am
Forum: Clarifications on Project Euler Problems
Topic: Problem 027
Replies: 26
Views: 12302

Re: Problem 027

If you'd care to elaborate on such a simple relationship @ PE.net, I would sure appreciate it, as I imagine Lucas-C would too... Take a look at hk's post on the first page of the problem's discussion forum. It shows the relationship between two solutions. If you plot all the related solutions (i.e....